Steiner tree problem with additional restriction were investigated. For example, the construction of minimum tree, where each path from the source node to the destination is the shortest. Since such problems are NP-hard, then a simple effective heuristic approach, based on the variation of one parameter, was proposed. The a priori bounds were calculated, as well as a special cases were found when the optimal solution could be constructed by polynomial time. The results of the investigations were published in the monograph, articles and reports.